A BSDE with default jump and unbounded terminal value arising in a Principal-Agent context

Jessica Martin ()
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Jessica Martin: INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse

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Abstract: Analysis of some problems from the field of Economics, called Principal-Agent problems, can lead to the derivation of a Backward Stochastic Differential Equation (BSDE) for which existence and uniqueness of solutions is required. In this paper, we tackle such an object in a setting where both a Brownian motion and default process co-exist. This BSDE is crucial for the analysis of Principal-Agent problems under a risk of economic shutdown as done in the companion paper [16] and the main departure from existing literature on similar equations such as [12] is an unbounded terminal condition. In order to deal with existence, we use a result from [14] to reduce the problem to proving existence of solutions to a solely Brownian BSDE for which we adapt the method of Briand and Hu from [2] using a key result from [12]. Uniqueness is then obtained through martingale properties of the process.

Date: 2021-01-11
Note: View the original document on HAL open archive server: https://hal.science/hal-03106006
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